Quadri-algebras
| dc.creator | Aguiar, Marcelo | |
| dc.creator | Loday, Jean-Louis | |
| dc.date | 2003-09-09 | |
| dc.date | 2004-04-05 | |
| dc.date.accessioned | 2026-07-07T05:01:00Z | |
| dc.date.available | 2026-07-07T05:01:00Z | |
| dc.description | We introduce the notion of quadri-algebras. These are associative algebras for which the multiplication can be decomposed as the sum of four operations in a certain coherent manner. We present several examples of quadri-algebras: the algebra of permutations, the shuffle algebra, tensor products of dendriform algebras. We show that a pair of commuting Baxter operators on an associative algebra gives rise to a canonical quadri-algebra structure on the underlying space of the algebra. The main example is provided by the algebra End(A) of linear endomorphisms of an infinitesimal bialgebra A. This algebra carries a canonical pair of commuting Baxter operators: $β(T)=T\ast\id$ and $γ(T)=\id\ast T$, where $\ast$ denotes the convolution of endomorphisms. It follows that End(A) is a quadri-algebra, whenever A is an infinitesimal bialgebra. We also discuss commutative quadri-algebras and state some conjectures on the free quadri-algebra. | |
| dc.identifier | https://arxiv.org/abs/math/0309171 | |
| dc.identifier | http://arxiv.org/abs/math/0309171 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68525 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17A30; 18D50 | |
| dc.title | Quadri-algebras | |
| dc.type | text |